Investigate the construction of a triangle in these portfolio activities. Use what you

Question

have learned about the Triangle Angle Sum Theorem and the Triangle Inequality
Theorem to create your submissions. Record your answers below.
Question 1
Find three objects (sticks, utensils, yarn, toys, books, etc.) that could represent
the sides of a triangle. Can you make a triangle with these three objects? Use the
Triangle Inequality Theorem explain why or why not.
(a) measurements of each object:
(b) Application of Triangle Inequality Theorem:

Answer 1

To investigate whether three objects can form a triangle, we need to use the Triangle Inequality Theorem, which states that for any triangle with side lengths \(a\), \(b\), and \(c\), the following conditions must be met:

1. \(a + b > c\)
2. \(a + c > b\)
3. \(b + c > a\)

In this exercise, I'll select three objects and apply the theorem.

Question 1

(a) Measurements of Each Object

1. Object 1 (Stick): Length = 5 cm
2. Object 2 (Stick): Length = 7 cm
3. Object 3 (Stick): Length = 10 cm

(b) Application of Triangle Inequality Theorem

Now, we will check the conditions of the Triangle Inequality Theorem:

1. \(5 + 7 > 10\)

   • Calculation: \(12 > 10\) (True)

2. \(5 + 10 > 7\)

   • Calculation: \(15 > 7\) (True)

3. \(7 + 10 > 5\)

   • Calculation: \(17 > 5\) (True)

Since all three conditions of the Triangle Inequality Theorem are satisfied, we can conclude that these three objects can indeed form a triangle.

Conclusion: Yes, we can make a triangle with these three objects, as they meet the criteria set by the Triangle Inequality Theorem.